Soft materials made up of tricked-up hard particles

Materials are made of smaller objects which in turn are made of smaller objects which in turn… For chemists, this hierarchy of scales usually stops when you eventually get down to atoms. However, well before that small scale, we treat some of these objects as particles (perhaps nano particles or colloids) that are clearly distinguishable and whose interactions may somehow be averaged (that is, coarse-grained) over the smaller scales. This gives rise to all sorts of interesting questions about how they are made and what they do once made. One of these questions concerns the structure and behavior of these particles if their mutual interactions is soft, that is when they behave as squishy balls when they get close to each other and unlike squishy balls continue to interact even when they are far away. This is quite different from hard interactions, that is when they behave like billiard balls that don’t overlap but don’t feel each other when they aren’t touching.

I previously blogged about our work showing that in one-dimension, we could mimic the structure of assemblies of soft particles using hard particles if only the latter were allowed to overlap (ghostlike) with some prescribed probability. In one dimension, this was like looking at a system of rods on a line. We wondered whether this was also possible in two dimensions (disks floating on a surface) or in three dimensions (balls in space). In our recent article, we confirmed that this overlapping (i.e. interpenetrable) hard-sphere model does indeed mimic soft particles in all three dimensions. This is particularly nice because the stochastic hard-sphere model is a lot easier to simulate and to solve using theoretical/analytical approaches. For example, we found a formula for the effective occupied volume directly from knowing the “softness” in the stochastic hard-sphere model.

The work was done in collaboration with my group members, Galen Craven and Alexander V. Popov. The title is "Structure of a tractable stochastic mimic of soft particles" and the work was funded by the National Science Foundation. It was released just this week at Soft Matter, 2014, Advance Article (doi:10.1039/C4SM00751D). It's already available as an Advance Article on the RSC web site, though this link should remain valid once it is formally printed.